Abstract: New analytical equations are derived for the three-dimensional gravity assist based on the patched conics model, including the variations in velocity, angular momentum, energy and inclination of the spacecraft due to the gravity assist. The equations developed here are verified by numerical integrations, using the circular restricted three-body problem, showing a good agreement better than 0.01. The results predicted by these analytical equations and the results computed by the numerical method differ by less than 0.7% under most conditions. This is a good indication that the analytical equations are good approximations and can be used for preliminary mission design. The influence of the parameters on the orbit of spacecraft is discussed based on the simplified equations which are the approximations of the above equations.